CFG Recognition (CFG Problems)

Description

Given a grammar $G$ and a string $s$, determine if the string $s$ can be derived by the grammar $G$.

Related Problems

Related: CFG Parsing

Parameters

n: length of the given string

Table of Algorithms

Name	Year	Time	Space	Approximation Factor	Model	Reference
Cocke–Younger–Kasami algorithm	1968	G|)$	$O(n^{2})$	Exact	Deterministic	Time & Space
Valiant	1975	G|)$ where omega is the exponent for matrix multiplication	$O(n^{2})$?	Exact	Deterministic	Time

Time Complexity graph

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Space Complexity graph

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Pareto Decades graph

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Reductions FROM Problem

Problem	Implication	Year	Citation	Reduction
k-Clique	assume: k-Clique Hypothesis then: there is no $O(N^{\omega-\epsilon}) time algorithm for target for any $\epsilon > {0}$	2017	https://ieeexplore-ieee-org.ezproxy.canberra.edu.au/abstract/document/8104058	link
k-Clique	assume: k-Clique Hypothesis then: there is no $O(N^{\{3}-\epsilon}) time combinatorial algorithm for target for any $\epsilon > {0}$	2017	https://ieeexplore-ieee-org.ezproxy.canberra.edu.au/abstract/document/8104058	link

References/Citation

https://linkinghub-elsevier-com.ezproxy.canberra.edu.au/retrieve/pii/S0022000075800468